we would like to visit the great wall. How can we go to Mutianyu section by using the subway.

I'm afraid the subway is not directly connected with Mutianyu, so you have to transfer to bus to get there. My suggestion is that take Beijing subway to Dongzhimen Station, where transfer to bus No. 916 or 916快 (express line) which go from Dongzhimen to Huairou Bus Station first, get off at Qingchun Lu Beikou, Huairou Bei Dajie or the terminus and then hire a mini-bus to Mutianyu.